Self-diagnosis devices for microcomputer-controlled network devices are already known, for instance from German Patent Disclosure Documents Nos. DE-OS 28 24 190, (and corresponding U.S. Pat. No. 4,267,569) DE-OS 29 22 371, and DE-OS 31 21 645. In these known systems, once an error is detected a corresponding data word is stored in a memory of the network device itself, and it can then be read and evaluated, for instance by a testing mechanic, in a repair facility using additional devices. To this end, a complicated serial interface is required, which many microcomputer systems do not initially have, and/or complicated additional devices are needed for performing the evaluation. These devices, in turn, must usually include a microcomputer. With each new network device, such systems must be altered and adapted accordingly, which is expensive.